Logically injuries to your ship's crew makes more sense as a percentage, especially when modified by your ship's mass (smaller ships get whacked harder due to a lack of inertia).

The problems are:
1.) Too much crew damage comes through shields. You should NOT be losing vast swaths of your crew when your shields are still up.
2.) Crew recovery rates are absolute rather than relative: you recover 1 person per second during combat. Obviously this is completely negligible for a ship with a crew of thousands.

Solutions:
1.) Damage to crew is reduced by 90% while shields are up, just like the kinetic damage from the torpedoes that generally cause this crew loss.
2.) Crew recovery rate should be percentage based so that large-crew ships are not punished.

It does not make perfect sense logically. A larger vessel would have more armor and mass between crew and attacker so even though you have a higher percentage chance of injuring someone the actual amount injured may well be less.

As you suggest however, if we MUST use this percentage based system then it should go both ways. As there is far more crew there would be far more medical staff and crewmen to get these injured to sickbay and back up and running.